On the computational complexity of ordinary differential equations
Information and Control
The complexity of analog computation
Mathematics and Computers in Simulation
The emperor's new mind: concerning computers, minds, and the laws of physics
The emperor's new mind: concerning computers, minds, and the laws of physics
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Complexity and real computation
Complexity and real computation
Computable analysis: an introduction
Computable analysis: an introduction
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
Classical physics and the Church--Turing Thesis
Journal of the ACM (JACM)
Upper and Lower Bounds on Continuous-Time Computation
UMC '00 Proceedings of the Second International Conference on Unconventional Models of Computation
Real recursive functions and their hierarchy
Journal of Complexity
Recursive Analysis Characterized as a Class of Real Recursive Functions
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Type-2 Computability and Moore's Recursive Functions
Electronic Notes in Theoretical Computer Science (ENTCS)
Polynomial time computation in the context of recursive analysis
FOPARA'09 Proceedings of the First international conference on Foundational and practical aspects of resource analysis
A characterization of computable analysis on unbounded domains using differential equations
Information and Computation
A survey of recursive analysis and Moore's notion of real computation
Natural Computing: an international journal
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We present a redevelopment of the theory of real-valued recursive functions that was introduced by C. Moore in 1996 by analogy with the standard formulation of the integer-valued recursive functions. While his work opened a new line of research on analog computation, the original paper contained some technical inaccuracies. We discuss possible attempts to remove the ambiguity in the behavior of the operators on partial functions, with a focus on his “primitive recursive” functions generated by the differential recursion operator that solves initial value problems. Under a reasonable reformulation, the functions in this class are shown to be analytic and computable in a strong sense in computable analysis. Despite this well-behavedness, the class turns out to be too big to have the originally purported relation to differentially algebraic functions, and hence to C. E. Shannon's model of analog computation.